PROBLEM STATEMENT: Imagine that each diagram in this activity represents a rug. A trap door opens directly over the rug and a dart falls down, landing at random somewhere on the rug. “At random” means that every point on the rug has a good chance of getting hit as every other point. PROCESS: Describe what you did in attempting to solve the problem. Do this part even if you did not solve the problem.
If you were trying to predict which part of this rug will get hit, which color would you choose, gray or white? What is the probability of getting hit for each color?
Since the square-shaped rug can be split into even pieces, I divided it into 12 pieces. 3 rows and 4 columns, depending on where the lines were and then creating more lines of similar length from each other. I then counted the colored squares. SOLUTION: State the solution clearly as you can. Explain how you know your answer is correct.
After counting the colored squares, I found that gray had 7/12 of the squares, and white had 5/12. The probability of being hit is 2/12 (or 1/6) more than landing on white. I can prove this answer is correct because since gray has more surface area than white, it has a greater chance of being hit by the dart.
I used this method to find the solution for every other carpet in this problem. EVALUATION: Discuss your personal reaction to the problem.
What did you learn from it?
Describe one Habit of a Mathematician that you used?
How would you change the problem to make it better?
Did you enjoy working on it?
Was it too hard or too easy?
During this project I learned to not assume something is more likely to happen because of the size, because you could be overestimating and could be wrong.
A habit of a mathematician that I used during this project was finding patterns. I used this during the line drawing process so I could make sure I was making accurate drawings and not messing anything up.
I would change the problem by making the first carpet a little easier to understand. Some of the other carpet problems included marks where you could draw lines and make even separations, but the first ones didn’t.
I enjoyed working on this problem. It was fun and challenging once you got to the more complicated carpets.
It seemed easy at the beginning, but after the 2nd or 3rd carpet it got challenging. I figured it out pretty quick once I knew what algorithms to use in the pattern making.